How can I disperse objects with a particle system?
It's possible that your particles are simply not big enough to see. If you can see them in the viewport, it should render fine.

Also, you don't need hair to instance object(s) on particles, you can do it with normal Emitted particles (to make them static, set the Normal velocity to 0 and also the Gravity weight to 0.

If you still have no luck, try it in an older version of blender (with Emitted particles, not hair) and see if that works. If it does, it's likely a bug that you should report.